Nadia is 20 years older than Ishaan. Twelve years ago, Nadia was 3 times as old as Ishaan. How old is Ishaan now?
Solution: We can use the given information to write down two equations that describe the ages of Nadia and Ishaan. Let Nadia's current age be $n$ and Ishaan's current age be $i$ The information in the first sentence can be expressed in the following equation: $n = i + 20$ Twelve years ago, Nadia was $n - 12$ years old, and Ishaan was $i - 12$ years old. The information in the second sentence can be expressed in the following equation: $n - 12 = 3(i - 12)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $i$ , it might be easiest to use our first equation for $n$ and substitute it into our second equation. Our first equation is: $n = i + 20$ . Substituting this into our second equation, we get the equation: $(i + 20)$ $-$ $12 = 3(i - 12)$ which combines the information about $i$ from both of our original equations. Simplifying both sides of this equation, we get: $i + 8 = 3 i - 36$ Solving for $i$ , we get: $2 i = 44$ $i = 22$.